Question

solve
find joint equation......
plz solutions write​

Answer 1

Answer:

$\boxed{ \huge{a) {x}^{2} - 3 {y}^{2} = 0}}$

Step-by-step explanation:

$\bold{ \underline{ \pink{To \: find}}} \longrightarrow \\ combined \: equation \: of \: line \: through \: origin \: each \: of \: which \: \\ makes \: an \: angle \: of \: 60 ^{ \circ} with \: y \: axis$

$\bold{ \underline{ \blue{Concept \: used}}} \longrightarrow \\ equation \: of \: line \: through \: origin \\ y = mx$

$\bold{ \underline{ \green{Solution}}} \longrightarrow \\ lines \: made \: angle \: of \: 60 ^{ \circ} \: with \: y \: axis \\ angle \: made \: by \: line \: (1) \: from \: x \: axis \\ = {90}^{ \circ} - {60}^{ \circ} \\ = {30}^{ \circ} \\ now \: equation \: of \: line \\ (1) \\ y = m(1)x \\ y = tan {30}^{ \circ} x \\ y = \dfrac{1}{ \sqrt{3} } x \\ \sqrt{3} y = x \\ \sqrt{3y } - x = 0 \\ angle \: made \: by \: second \: line \: from \: x \: axis \: \\ = {90}^{ \circ} + {60}^{ \circ} \\ = {150}^{ \circ} \\ equation \: of \: line \: (2) \\ y = m(2)x \\ y = tan {150}^{ \circ} x \\ y = - \dfrac{1}{ \sqrt{3} } x \\ \sqrt{3} y = - x \\ \sqrt{3} y + x = 0 \\ now \: combined \: equation \: of \: line \\ ( \sqrt{3} y + x)( \sqrt{3} y - x) = 0 \\ ( \sqrt{3} y) ^{2} - {(x)}^{2} = 0 \\ 3 {y}^{2} - {x}^{2} = 0 \\ chaning \: the \: sign \: of \: whole \: equation$

${x}^{2} - 3 {y}^{2} = 0$

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